论文标题
一般相对论中保守的非额外费用：物理定义与Noether的第二个定理
Conserved non-Noether charge in general relativity: Physical definition vs. Noether's 2nd theorem
论文作者
论文摘要
在本文中，我们对一般相对论中能量/熵的协变量进行了仔细的比较，该协作最近提出了包括当前作者在内的合作，与现有的能量定义，例如伪张量和准局部能量的能量。我们表明，一般相对性中能量的现有定义是Noether第二个定理的一般坐标转换定理的保守电荷，其保护性仅由局部对称性暗示，并且始终在不使用运动方程的情况下保持。因此，一般相对论中的现有定义都不反映系统的动力学特性，需要对能量的物理定义。相比之下，我们对总体相对论的能量/熵的新定义通常是一种保守的非额外电荷，并为各种情况（例如黑洞质量，重力崩溃和扩展的宇宙）提供身体上明智的结果，而现有的定义有时会导致零体的零元素，包括零和无限。我们得出的结论是，我们的建议比现有的能量定义更为物理。我们的提议使几乎唯一地定义了一般相对论的协变量和保守的能量/熵，这为未来的研究带来了一些影响。
In this paper, we make a close comparison of a covariant definition of an energy/entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from the pseudo-tensor and the quasi-local energy. We show that existing definitions of energies in general relativity are conserved charges from the Noether's 2nd theorem for the general coordinate transformation, whose conservations are merely identities implied by the local symmetry and always hold without using equations of motion. Thus none of existing definitions in general relativity reflects the dynamical properties of the system, need for a physical definition of an energy. In contrast, our new definition of the energy/entropy in general relativity is generically a conserved non-Noether charge and gives physically sensible results for various cases such as the black hole mass, the gravitational collapse, and the expanding universe, while existing definitions sometimes lead to unphysical ones including zero and infinity. We conclude that our proposal is more physical than existing definitions of energies. Our proposal makes it possible to define almost uniquely the covariant and conserved energy/entropy in general relativity, which brings some implications to future investigations.
